Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2013 |
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(9,11)(12,14,16,13)(15,17,19,18);(2,3)(5,7)(8,9)(10,11)(12,13,16,14)(15,18,19,17);(4,5)(6,7)(13,17)(14,18)(15,19)Polycyclic presentation:
2^7,3|b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,e^b=eg,h^b=h^2,d^c=dg,e^c=eg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10682696, #10682698, #10683974, … |
| maximal normal subgroup of | #10682696, #10682698, #10683974, … |
| maximal quotient of | #10695627, #10695641, #10695743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2237);